Glenn Gabe on Twitter pointed to a video hangout from last month where Google's John Mueller answered that specific question. At the 33:48 mark into the video, John said that is not how search works - Google doesn't have quota for web sites. It is not how search works, not how searchers work, etc.
Here is the video embed at the start time:
Here is the transcript:
Would you say the amount of users that can go through Google to my page on my site overall be a giant generic queries is adjusted based on the site quality signals and links. Like 5,000 visitors daily based on links and 5,000 visitors daily based on other site quality signals. Or is it more mix that you take together links and high-quality signals and say okay 10,000 visitors daily for the site overall?
So this kind of touches upon a misconception I see every now and then in that we don't have a quota for websites. We don't say 5,000 visitors this day, seven thousand visitors the next day. That's not how search works, that's not how users work. Sometimes people search more, sometimes people search less. Sometimes your site is more relevant, sometimes it's the less relevant.
There's no quota.
There's nothing where we would say oh we will send five hundred visitors today and when we reach 500 will stop sending traffic. That's not how search works.